Toni Schneidereit

Slavomira Schneidereit, Ashkan Mansouri Yarahmadi, Toni Schneidereit et al.

In this paper we extensively explore the suitability of YOLO architectures to monitor the process flow across a Fischertechnik industry 4.0 application. Specifically, different YOLO architectures in terms of size and complexity design along with different prior-shapes assignment strategies are adopted. To simulate the real world factory environment, we prepared a rich dataset augmented with different distortions that highly enhance and in some cases degrade our image qualities. The degradation is performed to account for environmental variations and enhancements opt to compensate the color correlations that we face while preparing our dataset. The analysis of our conducted experiments shows the effectiveness of the presented approach evaluated using different measures along with the training and validation strategies that we tailored to tackle the unavoidable color correlations that the problem at hand inherits by nature.

Sascha Emanuel Zell, Toni Schneidereit, Armin Fügenschuh et al.

Drowning is an omnipresent risk associated with any activity on or in the water, and rescuing a drowning person is particularly challenging because of the time pressure, making a short response time important. Further complicating water rescue are unsupervised and extensive swimming areas, precise localization of the target, and the transport of rescue personnel. Technical innovations can provide a remedy: We propose an Unmanned Aircraft System (UAS), also known as a drone-in-a-box system, consisting of a fleet of Unmanned Aerial Vehicles (UAVs) allocated to purpose-built hangars near swimming areas. In an emergency, the UAS can be deployed in addition to Standard Rescue Operation (SRO) equipment to locate the distressed person early by performing a fully automated Search and Rescue (S&R) operation and dropping a flotation device. In this paper, we address automatically locating distressed swimmers using the image-based object detection architecture You Only Look Once (YOLO). We present a dataset created for this application and outline the training process. We evaluate the performance of YOLO versions 3, 5, and 8 and architecture sizes (nano, extra-large) using Mean Average Precision (mAP) metrics mAP@.5 and mAP@.5:.95. Furthermore, we present two Discrete-Event Simulation (DES) approaches to simulate response times of SRO and UAS-based water rescue. This enables estimation of time savings relative to SRO when selecting the UAS configuration (type, number, and location of UAVs and hangars). Computational experiments for a test area in the Lusatian Lake District, Germany, show that UAS assistance shortens response time. Even a small UAS with two hangars, each containing one UAV, reduces response time by a factor of five compared to SRO.

Toni Schneidereit, Stefan Gohrenz, Michael Breuß

AI-based object detection, and efforts to explain and investigate their characteristics, is a topic of high interest. The impact of, e.g., complex background structures with similar appearances as the objects of interest, on the detection accuracy and, beforehand, the necessary dataset composition are topics of ongoing research. In this paper, we present a systematic investigation of background influences and different features of the object to be detected. The latter includes various materials and surfaces, partially transparent and with shiny reflections in the context of an Industry 4.0 learning factory. Different YOLOv8 models have been trained for each of the materials on different sized datasets, where the appearance was the only changing parameter. In the end, similar characteristics tend to show different behaviours and sometimes unexpected results. While some background components tend to be detected, others with the same features are not part of the detection. Additionally, some more precise conclusions can be drawn from the results. Therefore, we contribute a challenging dataset with detailed investigations on 92 trained YOLO models, addressing some issues on the detection accuracy and possible overfitting.

Santosh Humagain, Toni Schneidereit

Physics-informed neural networks approach the approximation of differential equations by directly incorporating their structure and given conditions in a loss function. This enables conditions like, e.g., invariants to be easily added during the modelling phase. In addition, the approach can be considered as mesh free and can be utilised to compute solutions on arbitrary grids after the training phase. Therefore, physics-informed neural networks are emerging as a promising alternative to solving differential equations with methods from numerical mathematics. However, their performance highly depends on a large variety of factors. In this paper, we systematically investigate and evaluate a core component of the approach, namely the training point distribution. We test two ordinary and two partial differential equations with five strategies for training data generation and shallow network architectures, with one and two hidden layers. In addition to common distributions, we introduce sine-based training points, which are motivated by the construction of Chebyshev nodes. The results are challenged by using certain parameter combinations like, e.g., random and fixed-seed weight initialisation for reproducibility. The results show the impact of the training point distributions on the solution accuracy and we find evidence that they are connected to the characteristics of the differential equation.

Toni Schneidereit, Michael Breuß

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent differential equations, one can apply the recently developed method of domain fragmentation. That is, the domain may be split into several subdomains, on which the optimisation problem is solved. In classic adaptive numerical methods, the mesh as well as the domain may be refined or decomposed, respectively, in order to improve accuracy. Also the degree of approximation accuracy may be adapted. It would be desirable to transfer such important and successful strategies to the field of neural network based solutions. In the present work, we propose a novel adaptive neural approach to meet this aim for solving time-dependent problems. To this end, each subdomain is reduced in size until the optimisation is resolved up to a predefined training accuracy. In addition, while the neural networks employed are by default small, we propose a means to adjust also the number of neurons in an adaptive way. We introduce conditions to automatically confirm the solution reliability and optimise computational parameters whenever it is necessary. Results are provided for several initial value problems that illustrate important computational properties of the method alongside. In total, our approach not only allows to analyse in high detail the relation between network error and numerical accuracy. The new approach also allows reliable neural network solutions over large computational domains.

Toni Schneidereit, Michael Breuß

Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include them directly in the cost function. Used within the corresponding neural network, the trial solutions define the so-called neural form. Such neural forms represent general, flexible tools by which one may solve various differential equations. In this article we consider time-dependent initial value problems, which require to set up the neural form framework adequately. The neural forms presented up to now in the literature for such a setting can be considered as first order polynomials. In this work we propose to extend the polynomial order of the neural forms. The novel collocation-type construction includes several feedforward neural networks, one for each order. Additionally, we propose the fragmentation of the computational domain into subdomains. The neural forms are solved on each subdomain, whereas the interfacing grid points overlap in order to provide initial values over the whole fragmentation. We illustrate in experiments that the combination of collocation neural forms of higher order and the domain fragmentation allows to solve initial value problems over large domains with high accuracy and reliability.

Toni Schneidereit, Michael Breuß

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature. Computational approaches are in general highly dependent on a variety of computational parameters as well as on the choice of optimisation methods, a point that has to be seen together with the structure of the cost function. The intention of this paper is to make a step towards resolving these open issues. To this end we study here the solution of a simple but fundamental stiff ordinary differential equation modelling a damped system. We consider two computational approaches for solving differential equations by neural forms. These are the classic but still actual method of trial solutions defining the cost function, and a recent direct construction of the cost function related to the trial solution method. Let us note that the settings we study can easily be applied more generally, including solution of partial differential equations. By a very detailed computational study we show that it is possible to identify preferable choices to be made for parameters and methods. We also illuminate some interesting effects that are observable in the neural network simulations. Overall we extend the current literature in the field by showing what can be done in order to obtain reliable and accurate results by the neural network approach. By doing this we illustrate the importance of a careful choice of the computational setup.